Thanks Cando, Sparrett & Jennaya;
1. The Plumber William Norman who lived in Clarendon St South Melb was not the family William although it's uncanny that he was living in Clarendon St which is the address that Jessie Norman gave on the ledger entry for her marriage. This William Norman died in 1890 some nine years after the family William Norman and unlike my Normans there are numerous other records of his life (Port Philip Electoral Roll and Argus Newspaper entries).
(The link to William Norman Plumber death 1890
http://www.rootschat.com/links/0y5i/ )
2. I get the impression that William Norman spent most of his life away from Australia serving with the RN and only returned in the late 1870's. There are certainly no records of William & Eliza having any further children and their death certificates list only the same children that came to Australia and the death of Fanny in Malta. The informant for the death of William and Eliza was in both cases their son William.
3. I have spent much time at the North Melbourne records office examining the large original ledger books form the Ballarat & Sunbury asylums trying to find the record for the Emily Norman who died at Ballarat in 1907 but to no avail. The problem I found was that this Emily Norman's name was included on the Male index not the Female but I could not find the actual entry in either case books (there are actually about 7 case books). Her age given as 52 would place the DOB at 1855 which is a bit later but then again her true age may not have been known, I have the ledger entry for this death in 1907 and it sheds no light at all as all her details are unknown. Her brother William and sister Jessie were both still alive in 1907 and I thought that they would have known or been contacts. By the way these old asylum case books are not light reading and come complete with before and after photos of those that made it through!
4. I did not know about the Kew entry so I will follow this one up
5. I'm not confident that the Emerald Hill rate books will reveal anything as the family may have been living with someone else who is listed as the rate payer.
6. I should point out that I have also gone through the census records in the UK looking for Emily XXX born Malta without any success, there is an Emily Weir of exactly the right age whose death is registered at Medway which includes Chatham where William Norman's father John came from (the Normans were mariners). The parents of William Norman Snr were John Norman and Sarah Wilson.
Thanks for all your efforts but this is a really hard one.
The records in Australia especially Victoria & NSW are very good but not perfect, I've already traced three family members one of whom is buried in the MGC that do not show up in the Vic BDM index, not to say they are not in the original ledgers though.